<div class="problemindexholder" problemindex="C">
 <div class="ttypography">
  <div class="problem-statement">
   <div class="header">
    <div class="title">
     C. Arpa and a game with Mojtaba
    </div>
    <div class="time-limit">
     <div class="property-title">
      time limit per test
     </div>
     1 second
    </div>
    <div class="memory-limit">
     <div class="property-title">
      memory limit per test
     </div>
     256 megabytes
    </div>
    <div class="input-file">
     <div class="property-title">
      input
     </div>
     standard input
    </div>
    <div class="output-file">
     <div class="property-title">
      output
     </div>
     standard output
    </div>
   </div>
   <div>
    <p>
     Mojtaba and Arpa are playing a game. They have a list of
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     numbers in the game.
    </p>
    <p>
     In a player's turn, he chooses a number
     <span class="tex-span">
      <i>
       p
      </i>
      <sup class="upper-index">
       <i>
        k
       </i>
      </sup>
     </span>
     (where
     <span class="tex-span">
      <i>
       p
      </i>
     </span>
     is a prime number and
     <span class="tex-span">
      <i>
       k
      </i>
     </span>
     is a positive integer) such that
     <span class="tex-span">
      <i>
       p
      </i>
      <sup class="upper-index">
       <i>
        k
       </i>
      </sup>
     </span>
     divides at least one number in the list. For each number in the list divisible by
     <span class="tex-span">
      <i>
       p
      </i>
      <sup class="upper-index">
       <i>
        k
       </i>
      </sup>
     </span>
     , call it
     <span class="tex-span">
      <i>
       x
      </i>
     </span>
     , the player will delete
     <span class="tex-span">
      <i>
       x
      </i>
     </span>
     and add
     <img align="middle" class="tex-formula" src="/predownloaded/ab/c1/abc163cc4cfcec983438bd883eb42fa05e15199b.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     to the list. The player who can not make a valid choice of
     <span class="tex-span">
      <i>
       p
      </i>
     </span>
     and
     <span class="tex-span">
      <i>
       k
      </i>
     </span>
     loses.
    </p>
    <p>
     Mojtaba starts the game and the players alternatively make moves. Determine which one of players will be the winner if both players play optimally.
    </p>
   </div>
   <div class="input-specification">
    <div class="section-title">
     Input
    </div>
    <p>
     The first line contains a single integer
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     (
     <span class="tex-span">
      1 ≤
      <i>
       n
      </i>
      ≤ 100
     </span>
     ) — the number of elements in the list.
    </p>
    <p>
     The second line contains
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     integers
     <span class="tex-span">
      <i>
       a
      </i>
      <sub class="lower-index">
       1
      </sub>
      ,
      <i>
       a
      </i>
      <sub class="lower-index">
       2
      </sub>
      , ...,
      <i>
       a
      </i>
      <sub class="lower-index">
       <i>
        n
       </i>
      </sub>
     </span>
     (
     <span class="tex-span">
      1 ≤
      <i>
       a
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ≤ 10
      <sup class="upper-index">
       9
      </sup>
     </span>
     ) — the elements of the list.
    </p>
   </div>
   <div class="output-specification">
    <div class="section-title">
     Output
    </div>
    <p>
     If Mojtaba wins, print "
     <span class="tex-font-style-tt">
      Mojtaba
     </span>
     ", otherwise print "
     <span class="tex-font-style-tt">
      Arpa
     </span>
     " (without quotes).
    </p>
    <p>
     You can print each letter in any case (upper or lower).
    </p>
   </div>
   <div class="sample-tests">
    <div class="section-title">
     Examples
    </div>
    <div class="sample-test">
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>4<br/>1 1 1 1<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>Arpa<br/></pre>
     </div>
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>4<br/>1 1 17 17<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>Mojtaba<br/></pre>
     </div>
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>4<br/>1 1 17 289<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>Arpa<br/></pre>
     </div>
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>5<br/>1 2 3 4 5<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>Arpa<br/></pre>
     </div>
    </div>
   </div>
   <div class="note">
    <div class="section-title">
     Note
    </div>
    <p>
     In the first sample test, Mojtaba can't move.
    </p>
    <p>
     In the second sample test, Mojtaba chooses
     <span class="tex-span">
      <i>
       p
      </i>
      = 17
     </span>
     and
     <span class="tex-span">
      <i>
       k
      </i>
      = 1
     </span>
     , then the list changes to
     <span class="tex-span">
      [1, 1, 1, 1]
     </span>
     .
    </p>
    <p>
     In the third sample test, if Mojtaba chooses
     <span class="tex-span">
      <i>
       p
      </i>
      = 17
     </span>
     and
     <span class="tex-span">
      <i>
       k
      </i>
      = 1
     </span>
     , then Arpa chooses
     <span class="tex-span">
      <i>
       p
      </i>
      = 17
     </span>
     and
     <span class="tex-span">
      <i>
       k
      </i>
      = 1
     </span>
     and wins, if Mojtaba chooses
     <span class="tex-span">
      <i>
       p
      </i>
      = 17
     </span>
     and
     <span class="tex-span">
      <i>
       k
      </i>
      = 2
     </span>
     , then Arpa chooses
     <span class="tex-span">
      <i>
       p
      </i>
      = 17
     </span>
     and
     <span class="tex-span">
      <i>
       k
      </i>
      = 1
     </span>
     and wins.
    </p>
   </div>
  </div>
  <p>
  </p>
 </div>
</div>
